A Frenchman who arrives in London, will find Philosophy, like every Thing else, very much chang’d there. He had left the World a plenum, and he now finds it a vacuum. At Paris the Universe is seen, compos’d of Vortices of subtile Matter; but nothing like it is seen in London. In France, ‘tis the Pressure of the Moon that causes the Tides; but in England ‘tis the Sea that gravitates towards the Moon; so what when you think that the Moon should make it flood with us, those Gentlemen fancy it should be Ebb, which, very unluckily, cannot be prov’d. For to be able to do this, ‘tis necessary the Moon and the Tides should have been enquir’d into, at the very instant of the Creation.

A soil adapted to the growth of plants, is necessarily prepared and carefully preserved; and, in the necessary waste of land which is inhabited, the foundation is laid for future continents, in order to support the system of the living world.

In 'Concerning and System of the Earth, its Duration and Stability', a Dissertation presented to the Royal Society of Edinburgh (Mar-Apr 1785). The surviving Abstract is excerpted in Frank H. T. Rhodes, Richard O. Stone and Bruce D. Malamud (eds.), Language of the Earth: A Literary Anthology (2002, 2nd. ed. 2008), 110.

All Nature is linked together by invisible bonds and every organic creature, however low, however feeble, however dependent, is necessary to the well-being of some other among the myriad forms of life.

An evolution is a series of events that in itself as series is purely physical, — a set of necessary occurrences in the world of space and time. An egg develops into a chick; … a planet condenses from the fluid state, and develops the life that for millions of years makes it so wondrous a place. Look upon all these things descriptively, and you shall see nothing but matter moving instant after instant, each instant containing in its full description the necessity of passing over into the next. … But look at the whole appreciatively, historically, synthetically, as a musician listens to a symphony, as a spectator watches a drama. Now you shall seem to have seen, in phenomenal form, a story.

ENGINEER, in the military art, an able expert man, who, by a perfect knowledge in mathematics, delineates upon paper, or marks upon the ground, all sorts of forts, and other works proper for offence and defence. He should understand the art of fortification, so as to be able, not only to discover the defects of a place, but to find a remedy proper for them; as also how to make an attack upon, as well as to defend, the place. Engineers are extremely necessary for these purposes: wherefore it is requisite that, besides being ingenious, they should be brave in proportion. When at a siege the engineers have narrowly surveyed the place, they are to make their report to the general, by acquainting him which part they judge the weakest, and where approaches may be made with most success. Their business is also to delineate the lines of circumvallation and contravallation, taking all the advantages of the ground; to mark out the trenches, places of arms, batteries, and lodgments, taking care that none of their works be flanked or discovered from the place. After making a faithful report to the general of what is a-doing, the engineers are to demand a sufficient number of workmen and utensils, and whatever else is necessary.

Even mistaken hypotheses and theories are of use in leading to discoveries. This remark is true in all the sciences. The alchemists founded chemistry by pursuing chimerical problems and theories which are false. In physical science, which is more advanced than biology, we might still cite men of science who make great discoveries by relying on false theories. It seems, indeed, a necessary weakness of our mind to be able to reach truth only across a multitude of errors and obstacles.

I regret that it has been necessary for me in this lecture to administer such a large dose of four-dimensional geometry. I do not apologize, because I am really not responsible for the fact that nature in its most fundamental aspect is four-dimensional. Things are what they are; and it is useless to disguise the fact that “what things are” is often very difficult for our intellects to follow.

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I think I may fairly make two postulata. First, That food is necessary to the existence of man. Secondly, That the passion between the sexes is necessary and will remain nearly in its present state. These two laws ever since we have had any knowledge of mankind, appear to have been fixed laws of our nature; and, as we have not hitherto seen any alteration in them, we have no right to conclude that they will ever cease to be what they are now, without an immediate act of power in that Being who first arranged the system of the universe; and for the advantage of his creatures, still executes, according to fixed laws, all its various operations.

I want to put in something about Bernoulli’s numbers, in one of my Notes, as an example of how the implicit function may be worked out by the engine, without having been worked out by human head & hands first. Give me the necessary data & formulae.

If you want to find out anything from the theoretical physicists about the methods they use, I advise you to stick closely to one principle: don't listen to their words, fix your attention on their deeds. To him who is a discoverer in this field the products of his imagination appear so necessary and natural that he regards them, and would like to have them regarded by others, not as creations of thought but as given realities.

In fact, no opinion should be with fervour. No one holds with fervour that 7 x 8 = 56 because it can be shown to be the case. Fervour is only necessary in commending an opinion which is doubtful or demonstrably false.

Indeed, we need not look back half a century to times which many now living remember well, and see the wonderful advances in the sciences and arts which have been made within that period. Some of these have rendered the elements themselves subservient to the purposes of man, have harnessed them to the yoke of his labors and effected the great blessings of moderating his own, of accomplishing what was beyond his feeble force, and extending the comforts of life to a much enlarged circle, to those who had before known its necessaries only.

From paper 'Report of the Commissioners Appointed to Fix the Site of the University of Virginia' (Dec 1818), reprinted in Annual Report of the Board of Visitors of the University of Virginia for the Fiscal Year Ending May 31, 1879 (1879), 10. Collected in Commonwealth of Virginia, Annual Reports of Officers, Boards, and Institutions of the Commonwealth of Virginia, for the Year Ending September 30, 1879 (1879).

Induction. The mental operation by which from a number of individual instances, we arrive at a general law. The process, according to Hamilton, is only logically valid when all the instances included in the law are enumerated. This being seldom, if ever, possible, the conclusion of an Induction is usually liable to more or less uncertainty, and Induction is therefore incapable of giving us necessary (general) truths.

Instead of adjusting students to docile membership in whatever group they happen to be placed, we should equip them to cope with their environment, not be adjusted to it, to be willing to stand alone, if necessary, for what is right and true.

In speech, 'Education for Creativity in the Sciences', Conference at New York University, Washington Square. As quoted by Gene Currivan in 'I.Q. Tests Called Harmful to Pupil', New York Times (16 Jun 1963), 66.

It is not necessary to probe into the nature of things, as was done by those whom the Greeks call physici; nor need we be in alarm lest the Christian should be ignorant of the force and number of the elements—the motion, and order, and eclipses of the heavenly bodies; the form of the heavens; the species and the natures of animals, plants, stones, fountains, rivers, mountains; about chronology and distances; the signs of coming storms; and a thousand other things which those philosophers either have found out, or think they have found out. … It is enough for the Christian to believe that the only cause of all created things, whether heavenly or earthly … is the goodness of the Creator, the one true God.

In Marcus Dods (ed.), J.F. Shaw (trans.), The Enchiridion of Augustine, Chap. 9, collected in The Works of Aurelius Augustine, Bishop of Hippo: A new translation (1873), Vol. 9, 180-181. The physici are natural philosophers.

Laws, in their most general signification, are the necessary relations arising from the nature of things. In this sense all beings have their laws: the Deity His laws, the material world its laws, the intelligences superior to man their laws, the beasts their laws, man his laws.

Men in general are very slow to enter into what is reckoned a new thing; and there seems to be a very universal as well as great reluctance to undergo the drudgery of acquiring information that seems not to be absolutely necessary.

In The Commercial and Political Atlas: Representing, by Means of Stained Copper Charts, the Progress of the Commerce, Revenues, Expenditure and Debts of England During the Whole of the Eighteenth Century (1786, 1801), 29.

No nation can be really great unless it is great in peace, in industry, integrity, honesty. Skilled intelligence in civic affairs and industrial enterprises alike; the special ability of the artist, the man of letters, the man of science, and the man of business; the rigid determination to wrong no man, and to stand for righteousness—all these are necessary in a great nation.

Nurses that attend lying-in women ought to have provided, and in order, every thing that may be necessary for the woman, accoucheur, midwife, and child; such as linnen and cloaths, well aired and warm, for the woman and the bed, which she must know how to prepare when there is occasion; together with nutmeg, sugar, spirit of hartshorn, vinegar, Hungary water, white or brown caudle ready made, and a glyster-pipe fitted.

Out of all possible universes, the only one which can exist, in the sense that it can be known, is simply the one which satisfies the narrow conditions necessary for the development of intelligent life.

So many of the chemical reactions occurring in living systems have been shown to be catalytic processes occurring isothermally on the surface of specific proteins, referred to as enzymes, that it seems fairly safe to assume that all are of this nature and that the proteins are the necessary basis for carrying out the processes that we call life.

The chemist works along his own brilliant line of discovery and exposition; the astronomer has his special field to explore; the geologist has a well-defined sphere to occupy. It is manifest, however, that not one of these men can tell the whole tale, and make a complete story of creation. Another man is wanted. A man who, though not necessarily going into formal science, sees the whole idea, and speaks of it in its unity. This man is the theologian. He is not a chemist, an astronomer, a geologist, a botanist——he is more: he speaks of circles, not of segments; of principles, not of facts; of causes and purposes rather than of effects and appearances. Not that the latter are excluded from his study, but that they are so wisely included in it as to be put in their proper places.

The general mental qualification necessary for scientific advancement is that which is usually denominated “common sense,” though added to this, imagination, induction, and trained logic, either of common language or of mathematics, are important adjuncts.

From presidential address (24 Nov 1877) to the Philosophical Society of Washington. As cited by L.A. Bauer in his retiring president address (5 Dec 1908), 'The Instruments and Methods of Research', published in Philosophical Society of Washington Bulletin, 15, 103. Reprinted in William Crookes (ed.) The Chemical News and Journal of Industrial Science (30 Jul 1909), 59.

The only level of the hierarchy [of biological communities] that is both necessary and sufficient to meet all objectives is the ecosystem or some higher-level approach. The strategy selected should not only ensure the conservation of spotted owls, but all the intricate linkages that are associated with natural populations of spotted owls in naturally functioning ecosystems. Many of these are as yet unknown.

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Through the animal and vegetable kingdoms, Nature has scattered the seeds of life abroad with the most profuse and liberal hand; but has been comparatively sparing in the room and the nourishment necessary to rear them. The germs of existence contained in this spot of earth, if they could freely develop themselves, would fill millions of worlds in the course of a few thousand years. Necessity, that imperious all-pervading law of nature, restrains them within the prescribed bounds. The race of plants and the race of animals shrink under this great restrictive law; and man cannot by any efforts of reason escape from it.

To say that mind is a product or function of protoplasm, or of its molecular changes, is to use words to which we can attach no clear conception. You cannot have, in the whole, what does not exist in any of the parts; and those who argue thus should put forth a definite conception of matter, with clearly enunciated properties, and show, that the necessary result of a certain complex arrangement of the elements or atoms of that matter, will be the production of self-consciousness. There is no escape from this dilemma—either all matter is conscious, or consciousness is something distinct from matter, and in the latter case, its presence in material forms is a proof of the existence of conscious beings, outside of, and independent of, what we term matter. The foregoing considerations lead us to the very important conclusion, that matter is essentially force, and nothing but force; that matter, as popularly understood, does not exist, and is, in fact, philosophically inconceivable. When we touch matter, we only really experience sensations of resistance, implying repulsive force; and no other sense can give us such apparently solid proofs of the reality of matter, as touch does. This conclusion, if kept constantly present in the mind, will be found to have a most important bearing on almost every high scientific and philosophical problem, and especially on such as relate to our own conscious existence.

From address to the National Science Teachers’ Association convention (Apr 1966), 'What Is Science?', collected in Richard Phillips Feynman and Jeffrey Robbins (ed.), The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman (1999, 2005), 179.

We cannot see how the evidence afforded by the unquestioned progressive development of organised existence—crowned as it has been by the recent creation of the earth's greatest wonder, MAN, can be set aside, or its seemingly necessary result withheld for a moment. When Mr. Lyell finds, as a witty friend lately reported that there had been found, a silver-spoon in grauwacke, or a locomotive engine in mica-schist, then, but not sooner, shall we enrol ourselves disciples of the Cyclical Theory of Geological formations.

We have not done the things that are necessary to lower emissions because these things fundamentally conflict with deregulated capitalism… We are stuck because the actions that would give us the best chance of averting catastrophe–and would benefit the vast majority–are extremely threatening to an elite minority that has a stranglehold over our economy, our political process, and most of our major media outlets.

We may, I think, draw a yet higher and deeper teaching from the phenomena of degeneration. We seem to learn from it the absolute necessity of labour and effort, of struggle and difficulty, of discomfort and pain, as the condition of all progress, whether physical or mental, and that the lower the organism the more need there is of these ever-present stimuli, not only to effect progress, but to avoid retrogression. And if so, does not this afford us the nearest attainable solution of the great problem of the origin of evil? What we call evil is the essential condition of progress in the lower stages of the development of conscious organisms, and will only cease when the mind has become so thoroughly healthy, so well balanced, and so highly organised, that the happiness derived from mental activity, moral harmony, and the social affections, will itself be a sufficient stimulus to higher progress and to the attainment of a more perfect life.

We reverence ancient Greece as the cradle of western science. Here for the first time the world witnessed the miracle of a logical system which proceeded from step to step with such precision that every single one of its propositions was absolutely indubitable—I refer to Euclid’s geometry. This admirable triumph of reasoning gave the human intellect the necessary confidence in itself for its subsequent achievements. If Euclid failed to kindle your youthful enthusiasm, then you were not born to be a scientific thinker.

Well do I remember that dark hot little office in the hospital at Begumpett, with the necessary gleam of light coming in from under the eaves of the veranda. I did not allow the punka to be used because it blew about my dissected mosquitoes, which were partly examined without a cover-glass; and the result was that swarms of flies and of 'eye-flies' - minute little insects which try to get into one's ears and eyelids - tormented me at their pleasure

When rich men are thus brought to regard themselves as trustees, and poor men learn to be industrious, economical, temperate, self-denying, and diligent in the acquisition of knowledge, then the deplorable strife between capital and labor, tending to destroy their fundamental, necessary, and irrefragable harmony will cease, and the world will no longer be afflicted with such unnatural industrial conflicts as we have seen during the past century...

Address (31 May 1871) to the 12th annual commencement at the Cooper Union, honoring his 80th birthday, in New York City Mission and Tract Society, Annual report of the New York City Mission and Tract Society (1872), 69.

[D]iscovery should come as an adventure rather than as the result of a logical process of thought. Sharp, prolonged thinking is necessary that we may keep on the chosen road but it does not itself necessarily lead to discovery. The investigator must be ready and on the spot when the light comes from whatever direction.

[On gold, silver, mercury, platinum, palladium, rhodium, iridium, osmium:] As in their physical properties so in their chemical properties. Their affinities being weaker, (the noble metals) do not present that variety of combinations, belonging to the more common metals, which renders them so extensively useful in the arts; nor are they, in consequence, so necessary and important in the operations of nature. They do not assist in her hands in breaking down rocks and strata into soil, nor do they help man to make that soil productive or to collect for him its products.

[Young] was afterwards accustomed to say, that at no period of his life was he particularly fond of repeating experiments, or even of very frequently attempting to originate new ones; considering that, however necessary to the advancement of science, they demanded a great sacrifice of time, and that when the fact was once established, that time was better employed in considering the purposes to which it might be applied, or the principles which it might tend to elucidate.

In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- Carl Sagan